Related papers: Stochastic selection problem for a Stratonovich SD…
We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…
This paper considers the problem of uniqueness of the solutions to a class of Markovian backward stochastic differential equations (BSDEs) which are also connected to certain nonlinear partial differential equation (PDE) through a…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
We study the focusing stochastic nonlinear Schr\"odinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, in the $L^2$-critical and supercritical cases. The mass…
In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the…
We prove exponential convergence to the invariant measure, in the total variation norm, for solutions of SDEs driven by $\alpha$-stable noises in finite and in infinite dimensions. Two approaches are used. The first one is based on Harris…
In this paper, we develop a new general approach to the existence and uniqueness theory of infinite dimensional stochastic equations of the form dX+A(t)Xdt = XdW in (0;T)xH, where A(t) is a nonlinear monotone and demicontinuous operator…
The rate of strong convergence is investigated for an approximation scheme for a class of stochastic differential equations driven by a time-changed Brownian motion, where the random time changes $(E_t)_{t\ge 0}$ considered include the…
Stemmed from the derivation of the optimal control to a stochastic linear-quadratic control problem with Markov jumps, we study one kind of backward stochastic differential equations (BSDEs) that the generator f is affected by a Markovian…
We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form $d A_t =\mu (t, A_t) d t + \sigma(t, A_t) d W_t$. We provide sufficient conditions…
This article is concerned with the existence of solution to the stochastic Degasperis-Procesi equation on $\mathbb{R}$ with an infinite dimensional multiplicative noise and integrable initial data. Writing the equation as a system composed…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
We consider a stochastic heat equation driven by a space-time white noise and with a singular drift, where a local-time in space appears. The process we study has an explicit invariant measure of Gibbs type, with a non-convex potential. We…
Ambiguities in the functional-integral solution of the stochastic differential equation (SDE) arising due to the definition on the functional Jacobi determinant and the white-in-time limit in the noise are analyzed and two forms of the de…
We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type…
In this paper we consider a stochastic thin-film equation with a one dimensional Gaussian Stratonovych noise. We establish the existence of non-negative global weak martingale solution, and study its long time asymptotic properties. In…
We study stochastic approximation algorithms with Markovian noise and constant step-size $\alpha$. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between…
Let $d \ge 2$. In this paper, we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dS_{t}+b(s+t, X_{t})dt, \quad X_{0}=x, \] where $(s,x)\in \mathbb{R}_+ \times \mathbb{R}^{d}$ is the initial starting…